Abstract
In this paper we investigate the existence of ground states and dual ground states for Maxwell’s Equations in {mathbb {R}}^3 in nonlocal nonlinear metamaterials. We prove that several nonlocal models admit ground states in contrast to their local analogues.
Highlights
The existence of ground states is of central importance for a large number of linear and nonlinear time-independent models in physics
In this paper we are interested in ground states for the nonlinear Maxwell equations
(c) The existence of discontinuous and concentrating solutions illustrates that no regularity theory and no compact embeddings in whatever Lebesgue space can be exploited in the analysis of the nonlinear Maxwell equation (2)
Summary
The existence of ground states is of central importance for a large number of linear and nonlinear time-independent models in physics. The governing idea is that the physically most relevant nontrivial solution of a given PDE is the one with lowest energy. Such a solution is called a ground state. The symbols E, D : R3 → C3 denote the electric field and the electric induction whereas H, B : R3 → C3 represent the magnetic field and the magnetic induction, respectively. This overdetermined system is accompanied with constitutive relations that provide a link between these quantities. This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
